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Express the ratio 42 minutes to 0.1 hours in its simplest form.
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The two parts of this ratio have been given using different units.
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One side is expressed in minutes.
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And the other side is expressed in hours.
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In order to express this ratio in its simplest form, we need to convert both sides to the same unit.
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What is 0.1 hours in minutes?
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Well, one hour is equal to 60 minutes.
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We could approach this conversion in two different ways.
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We could keep the 0.1 as a decimal and work out 0.1 multiplied by 60.
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This is equivalent to working out 0.1 multiplied by 10 multiplied by six.
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0.1 multiplied by 10 is just one.
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So this is equivalent to one multiplied by six, which is six.
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The second approach would be to use fractions if you’re more comfortable working with these than decimals.
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0.1 is equivalent to one tenth.
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To find what one-tenth of 60 minutes is, we need to divide by 10.
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60 divided by 10 is equal to six.
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So using whichever method you’re more comfortable with, we’ve shown that 0.1 hours is equivalent to six minutes.
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So the ratio of 42 minutes to 0.1 hours can be written instead as 42 minutes to six minutes.
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The units on the two sides of the ratio are now the same.
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So they can be cancelled out.
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We’re left with a ratio of 42 to six.
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But this isn’t yet in its simplest form.
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42 and six both have a common factor of six.
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So both parts of the ratio can be divided by six.
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The ratio in its simplest form is seven to one.